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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos


2.12 Probability HOME | Objectives | Probability Review | Probability tables | Two Way Tables | Risk & Relative Risk | Tree Diagrams | Conditional Prob | Distributions | Actual vs Normal | Normal Distribution | Inverse Normal | Revision


Different Distributions

Uniform (flat) distribution:
6 sided dice simulation and a 6 to 30 sided dice

Triangular distribution
Sum of Two 6 sided simulation (horse race)

Drawing Distributions, mix and match,

Popcorn sound distribution
How greater data and narrower intervals approximates a bell shape curve.
Overview of the normal distribution curve.

Class notes, Blank notes

Interactive web site java simulation

Theta (new & old & workbook) Ex24.01



Normal Distribution Introduction

Calculation of the mean and standard deviation. Standard Deviation
Normal Distribution introduction and overview.
The effect of changing the mean and/or standard deviation

Measures of Centre & Spread

Normal Distribution | Normal Distribution | Comparing distributions


Standard Dev: Class notes | Blank notes
Normal: Class notes | Blank notes

Theta (new & old & workbook) Ex24.02 and Ex24.03


Histograph & Distributions

If a set of data is grouped and displayed using a histograph a distribution of the data is produced

Even distribution

No central tendancy
Skewed distribution

More data at lower values
Two regions of distribution

Two data bunches: around 20 and 40


Usually data sets display central tendancy (most data around some value) and a spread either side of this value.

One measure of central tendancy is the mean µ

One measure of spread is the standard deviation σ

A histograph or a set of 500 data values

With a population mean µ=10 and standard deviation of σ = 5

Reducing the interval width on the histograph

Note: all the areas add to a total of 1.0

And reducing the interval width more

Note: all the areas still add to a total of 1.0

The histograph can be approximated with the NORMAL DISTRIBUTION curve
There is a central tendancy and a symmetrical spread either side


With mean µ=10 and standard deviation of σ = 5

Note: the area under the graph equals 1.0


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